Electrostatic Potential & Capacitance

• Derive electric potential from electric field line integrals: V = -∫ E · dr.
• Analyze properties and geometries of equipotential surfaces.
• Derive capacitance formula for parallel plate capacitor with and without dielectric slabs.
• Calculate equivalent capacitance in series and parallel networks and energy density.

• Electric Potential due to Point Charge & Dipole (V = kp cos θ / r^2)
• Equipotential Surfaces & Field Orthogonality (E = -dV/dr)
• Capacitance Definition: C = Q / V
• Parallel Plate Capacitor: C = ε0 A / d (with Dielectric: C = K ε0 A / d)
• Energy Stored in Capacitor: U = 1/2 CV^2 = 1/2 Q^2/C

“Electric field is always oriented in the direction of steepest decreasing electrostatic potential.”

• •No work is required to move a charge across an equipotential surface.
• •When a dielectric slab is inserted with battery disconnected, charge Q remains constant while potential V drops.
• •Energy density in electric field: u_E = 1/2 ε0 E^2.

Numericals on complex capacitor circuits, dielectric insertion effects, and potential surfaces.